{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Further Hypothesis Testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "── Attaching packages ─────────────────────────────────────── tidyverse 1.3.0 ──\n",
      "✔ ggplot2 3.3.0     ✔ purrr   0.3.4\n",
      "✔ tibble  3.0.1     ✔ dplyr   0.8.5\n",
      "✔ tidyr   1.1.0     ✔ stringr 1.4.0\n",
      "✔ readr   1.3.1     ✔ forcats 0.4.0\n",
      "── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──\n",
      "✖ dplyr::filter() masks stats::filter()\n",
      "✖ dplyr::lag()    masks stats::lag()\n"
     ]
    }
   ],
   "source": [
    "# Select this cell and type Ctrl-Enter to execute the code below.\n",
    "\n",
    "library(tidyverse)\n",
    "\n",
    "set_plot_dimensions <- function(width_choice, height_choice) {\n",
    "    options(repr.plot.width=width_choice, repr.plot.height=height_choice)\n",
    "}\n",
    "\n",
    "cbPal <- c(\"#E69F00\", \"#56B4E9\", \"#009E73\", \"#F0E442\", \"#CC79A7\", \"#0072B2\", \"#D55E00\")\n",
    "\n",
    "set_plot_dimensions(5, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# You should see \"Attaching packages\" and some ticks by the packages loaded.\n",
    "# The \"Conflicts\" aren't a problem.\n",
    "\n",
    "# Other problems loading the library? Try running this cell.\n",
    "\n",
    "install.packages('tidyverse')\n",
    "\n",
    "library(tidyverse)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 - Comparing variances of two groups"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Parsed with column specification:\n",
      "cols(\n",
      "  temperature = col_double(),\n",
      "  luminosity = col_double(),\n",
      "  radius = col_double(),\n",
      "  spectral_class = col_character(),\n",
      "  type = col_double()\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "# Run this cell to load the data.\n",
    "\n",
    "data <- read_csv(\"stars.csv\")\n",
    "\n",
    "type_key <- c('Brown Dwarf', 'Red Dwarf', 'White Dwarf', 'Main Sequence', 'Supergiant','Hypergiant')\n",
    "spectral_classes <- c('O','B','A','F','G','K','M')\n",
    "\n",
    "data$type <- factor(data$type)\n",
    "data$spectral_class <- factor(data$spectral_class, levels=spectral_classes)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The t-test only compares the *means* of the two groups. \n",
    "Next, Dr Howe would like you to check their *variances*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question: do types 4 and 5 have the same variance in log(luminosity)?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q-Q plot\n",
    "\n",
    "The [*quantile-quantile plot*](https://en.wikipedia.org/wiki/Q–Q_plot) (Q-Q plot) is a simple, graphical method to check whether two sets of observations appear to come from the same distribution, or to compare one set of data to a theoretical distribution.\n",
    "\n",
    "It is made by plotting the quantiles (i.e. percentiles) of the two distributions against each other.\n",
    "\n",
    "If the variances are the same, the Q-Q plot will approximate a straight line with gradient 1.\n",
    "\n",
    "We can find the percentiles for our sample with the `quantile()` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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VSY7byST5HkDbQA7XOgTy8HN4QC+2bdl2t/Iut6VhYkEPQOtPnZ4grFLQozAn2I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\ngAACCCCAAAIIIIAAAggggEBhAv8fgNWmGWDC1/kAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "type4 <- \n",
    "    data %>% \n",
    "    filter(type == 4) %>% \n",
    "    pull(luminosity) %>% \n",
    "    log\n",
    "\n",
    "type5 <-\n",
    "    data %>% \n",
    "    filter(type == 5) %>% \n",
    "    pull(luminosity) %>% \n",
    "    log\n",
    "\n",
    "x <- seq(0, 1, 0.01)\n",
    "t4q <- quantile(type4, x)\n",
    "t5q <- quantile(type5, x)\n",
    "\n",
    "ymin <- 11\n",
    "ymax <- 14\n",
    "\n",
    "set_plot_dimensions(6, 4)\n",
    "par(mfrow=c(1,2))\n",
    "plot(x,t4q,col=cbPal[5],pch=16,ylim=c(ymin,ymax),ylab=\"type 4\")\n",
    "plot(x,t5q,col=cbPal[6],pch=16,ylim=c(ymin,ymax),ylab=\"type 5\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting type 5 against type 4:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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cAjMFqfN24FL23+K2n9GqfHPgZsvz59+sQk+HyxHgWi1+o7aCAai4zqI+BThNV3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\nrkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "set_plot_dimensions(5, 5)\n",
    "plot(t4q,t5q,col='grey',pch=16,xlab=\"type 4\",ylab=\"type 5\")\n",
    "\n",
    "# the line with gradient 1, passing through Q50:\n",
    "m <- 1\n",
    "c <- t5q[50] - t4q[50] * m\n",
    "lines(t4q, m * t4q + c, col='black')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This looks like a pretty good fit, but we can do an [*F-test*](https://en.wikipedia.org/wiki/F-test_of_equality_of_variances) to be more rigorous:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### F-test for equality of variances"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Theory\n",
    "\n",
    "Once again, we need a two-tailed test:\n",
    "\n",
    "$H_0$: The two populations have identical variance  $\\sigma^2 = \\sigma_1^2 = \\sigma_2^2$.\n",
    "\n",
    "$H_1$: The two populations have non-identical variances, $\\sigma_1^2 \\ne \\sigma_2^2$.\n",
    "\n",
    "The test statistic is simply the ratio of the sample variances:\n",
    "\n",
    "$$F = \\frac{s_1^2}{s_2^2}$$.\n",
    "\n",
    "Under $H_0$, $F$ follows an [*F-distribution*](https://en.wikipedia.org/wiki/F-distribution) with parameters $(n_1 - 1,n_2 - 1)$.\n",
    "\n",
    "We use this distribution to calculate a p-value for the observed value of the test statistic, $F$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Assumpions\n",
    "\n",
    "- The two samples both follow normal distributions.\n",
    "\n",
    "Note that the means of the two populations may differ.\n",
    "The F-test is highly sensitive to deviations from the assumption of normality.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Application\n",
    "\n",
    "We will set $\\alpha=0.05$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualise the F-distribution corresponding to our example ($n_1 = n_2 = 40$):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KyQlSCAAAIBFXA9wYrulrl6coHiBsWyyMTP9XiaoofCkqwuiomK9QpKOAUswWL8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\nsQ7xSzxw3QAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x <- seq(0.1,3,0.01)\n",
    "set_plot_dimensions(5, 4)\n",
    "plot(x,df(x,39,39), xlab=\"F\", ylab=\"pdf\", type=\"l\", col=\"grey\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will calculate the test statistic:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"F = 0.713975307250036\"\n"
     ]
    },
    {
     "data": {
      "image/png": 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hVRqvyBiXsSV5X60mkK1CIwfvz4SOi3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\nrkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fstat <- var(type4)/var(type5)\n",
    "print(paste(\"F =\",fstat))\n",
    "\n",
    "set_plot_dimensions(5, 4)\n",
    "plot(x,df(x,39,39), xlab=\"F\", ylab=\"pdf\", type=\"l\", col=\"grey\")\n",
    "\n",
    "x_region <- seq(0.1,fstat,0.01)\n",
    "polygon(c(x_region,fstat,0.01), c(df(x_region,39,39),0,0), border=NA, col=\"lightgrey\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the CDF to calculate the left-tail $p$-value and double it for a two-tailed test:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"p = 0.297027010291429\"\n"
     ]
    }
   ],
   "source": [
    "p_value <- pf(fstat,39,39) * 2\n",
    "print(paste(\"p =\",p_value))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, $p>\\alpha$ so we accept the null hypothesis of equal variance, at the 5% level.\n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
